Geodesic
Properties of Kagi and Renko Moments for Homogeneous Diffusion Processes
Matematičeskie zametki, Tome 91 (2012) no. 2, pp. 270-284

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For a homogeneous diffusion process $(X_t)_{t\geqslant 0}$, we consider problems related to the distribution of the stopping times \begin{gather*} \gamma_{\max}=\inf\Bigl\{t\ge 0:\sup_{s\le t}X_s-X_t \ge H\Bigr\},\qquad \gamma_{\min}=\inf \Bigl\{t\ge 0: X_t-\inf_{s\le t}X_s \ge H \Bigr\}, \\ \kappa_0=\inf\Bigl\{t\ge 0:\sup_{s\le t}X_s-\inf_{s\le t}X_s \ge H\Bigr\}. \end{gather*} The results obtained are used to construct an inductive procedure allowing us to find the distribution of the increments of the process $X$ between two adjacent kagi and renko instants of time.
Keywords: homogeneous diffusion process, Brownian motion, stopping time, kagi instant of time
Mots-clés : renko instant of time, Laplace transform. 
@article{MZM_2012_91_2_a8,
     author = {M. A. Spiryaev},
     title = {Properties of {Kagi} and {Renko} {Moments} for {Homogeneous} {Diffusion} {Processes}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {270--284},
     publisher = {mathdoc},
     volume = {91},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_91_2_a8/}
}
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M. A. Spiryaev. Properties of Kagi and Renko Moments for Homogeneous Diffusion Processes. Matematičeskie zametki, Tome 91 (2012) no. 2, pp. 270-284. http://geodesic.mathdoc.fr/item/MZM_2012_91_2_a8/